As a discipline or means of developing the mind, mathematical science may be intermediary, a method to teach the mind to pass from the sphere of sense to the sphere of ideas; but “mathematical numbers” are “ideal numbers,” that is, ideas. They are to be distinguished, of course, from “concrete numbered things.” We have in Plato “numbered things” and “ideal numbers,” but no third something between them.[1]
The Neoplatonists following Plato in his psychology follow him also in his method of mathematical demonstration. Plotinus says: “He (who would learn philosophy) must be instructed in the mathematical disciplines, in order that he may be accustomed to the perception of and belief in an incorporeal essence;”[2] “Geometry, which is conversant with intelligibles, must be arranged in the intelligible world.”[3]
The noted English deist and infidel, Thomas Taylor, an ardent student and great admirer of the Neoplatonists, understanding the use made by them of geometry, said a century ago: “We are surprised to find a use in geometry which at present it is by no means suspected to afford. For who would conceive that it is the genuine passage to true theology and the vestibule to divinity?”[4] We would not deny that it is a means of learning
